Questions tagged [quantum-chemistry]

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Quantum simulation of molecular spectroscopy: why?

Molecular spectroscopy, e.g. through light-matter interaction, is a powerful tool to measure molecular properties such as bond lengths, energy levels, vibration frequencies, ... which give insights ...
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Can you burn a quantum fluid?

Perhaps more generally, can you have a chemical reaction between a quantum fluid (a sodium Bose-Einstein condensate for example) and another quantum fluid or a non-quantum fluid? Or as a silly ...
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Is Hartree-Fock (HF) a ground state theory?

To calculate the orbitals in Hartree-Fock (HF) theory we imply the variations principle, so we try to find the wavefunction which minimises the energy $\left<\psi|H|\psi\right>$. This ...
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Why does Hartree-Fock (HF) theory even work?

Let’s say we have $N$ electrons and we want to derive the Hartree-Fock (HF) equations. The first step would be to define a Slater determinant of $N$ electrons: $$\psi(x_1,x_2,… x_N) = \frac{1}{\sqrt{...
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From molecular orbitals to band diagram

Let’s say we have a periodic crystal structure. We could, in theory, treat this system as if it were a large molecule. Therefore, we could use Hartree Fock theory or other methods to get the molecular ...
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Why is there no exchange interaction when there is no coulomb interaction?

The Hartree-Fock energy may be written as $$ E_{HF}= \langle\Psi| H |\Psi\rangle = \sum_{a} \langle a| h |a \rangle + \frac{1}{2}\sum_{ab} \big( [aa |bb] - [ab|ba] \big),$$ with the exchange term $$[...
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Classical optical activity parallel to the helical axis of a molecule/spring

The image below is from Kauzmann's Quantum Chemistry. It is an intuitive classical explanation of optical rotation due to light hitting a helical structure (usually a molecule) perpendicular to the ...
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General form of a fermionic Hamiltonian in second quantization

I am a new to quantum chemistry. I've been reading this paper and it seems like the equation (1) in the paper which is, $H = \sum_{pq} T_{pq} a_p^\dagger a_q + \sum_p U_pn_p + \sum_{pq} V_{pq} n_p n_q$...
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Ammonia electric dipole moment according to Philip Warren Anderson

In his paper "More is Different", Philip Warren Anderson claims to be in posession of a proof by which any stationary state of an Ammonia molecule (or anything really, again according to him,...
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What is the reason for Avagadro's Law?

From outside the quantum stuff I'm tiredelessly learning, I've been reminded about Avagadro's Law — i.e., the fact that any molecular gas has the same count of molecules in the same volume and ...
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Matrix Product States in terms of Hermite Polynomial Basis

So far, I've used MPS only for spin systems on a lattice (e.g. Ising, Heisenberg Model, etc. where I can grasp the MPS construction). Now, I'm faced with a situation where I have to use Hermite ...
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Energy calculated by second-quantized Hamiltonian doesn't match the Hartree Fock energy

Introduction¶$$\renewcommand{\ket}[1]{\left|{#1}\right\rangle}$$$$\renewcommand{\bra}[1]{\left\langle{#1}\right|}$$$$\renewcommand{\braket}[2]{\left\langle{#1}\middle|{#2}\right\rangle}$$Given a ...
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Potential Energy of the Helium Atom

So I just learned how to solve the Schroedinger Equation for the Hydrogen atom. The set up looked like this: $$\left[\dfrac{1}{r^2}\frac{\partial}{\partial r}\left(r^2\dfrac{\partial}{\partial r}\...
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How did the Aufbau principle come to be? [duplicate]

How did the Aufbau principle come to be? Being that my education on chemistry doesn't go past highschool, i was never sure how the following diagram was conceived: I would like to understand how the ...
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Energy of the singlet excited state for two-orbital system in Hartree Fock method

Say we have two orbitals $\epsilon_1$ and $\epsilon_2$ from RHF solution of a two-particle two-orbital system. If we place both electrons on $\epsilon_1$ we have the ground state. We can also place $\...
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Is it justified to take orbital as just a "dispersed region of charge" for applications in Organic chemistry?

When I read organic chemistry book in the past, it seems so a heuristic used to explain and understand reaction mechanism is that negative charge attracts positive charge (or indirectly as ...
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5 answers
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Separatibility of wave-function in Schrodinger equation describing motion of particle in spherical shell [closed]

Question. Why wave-function describing rotation of particle around spherical surface is separable? Why solution obtained assuming function is separable is general solution? I am interested in proof of ...
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Are there some references to periodic Hartree-Fock calculation?

I want to learn Hartree-Fock(HF) calculation for periodic system, but didn't find some reference. And also have some confusion about it now. In one book(Quantum Chemistry of Solids: The LCAO First ...
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Electrostatic self-interaction of two multivariate Gaussian charge densities

I'm trying to figure out the following question: If $\mathcal{N_1}(\vec x|\vec \mu_1, \Sigma_1)$ and $\mathcal{N_2}(\vec x|\vec \mu_2, \Sigma_2)$ are two arbitrary multivariate Gaussian charge ...
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Best computational method for describing the electronic configuration of an ion in a crystal structure

I have a question to ask you: does anyone know an accurate computational method to calculate the splitting of the d and/or f orbitals of a type of ions that are part of an ionic crystal? For example: ...
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potential energy of two atom Molecule in case of ionic bond

The formula for the potential energy of a two atomic Molecule in case of a ionic bond is given by: $$E_p(r)= -\frac{e^2}{4 \pi \epsilon_0 r} + \frac{b}{r^9}$$ What is the physical meaning of these ...
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What eigenstates of the Fock operator gives the Hartree Fock ground state?

In the Hartree Fock method with $N$ electrons, the Fock operator is a one-electron operator defined by $$f := h + \sum_{n=1}^N J_n - K_n,$$ where $h = -\frac{1}{2} \nabla^2 + V_{el-nu}$ is the one-...
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Multi-electron Bloch bundles over powers of the Brillouin torus?

The quantum states of single electrons in a crystal famously form a (Hilbert) vector bundle over the Brillouin torus ${\mathbb{T}}^d$ -- the Bloch bundle. Does this theory usefully generalize to ...
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Finding a bound on ground state energy derivatives of molecule

Part of a project I'm working on involves exploring the smoothness of the ground state energy $E(x)$ of a molecule where $E$ is parameterized by the geometry of the molecule. In particular, my goal ...
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What is the single active electron approximation?

I keep stumbling upon this approximation while reading papers on atomic physics, but I couldn't find a proper description of what it is in any textbook or pedagogical paper. The closest I could find ...
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QM: How do electrons affect each other's potential energy?

I'm trying to learn quantum mechanics. And I'm confused. The question is, do electrons affect each other's wave functions, i.e. potential energies? How do they affect each other orbital shapes, how do ...
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The uncertainty principle and the quantization of electron momentum in orbitals - Why are larger energy gaps considered more uncertain?

I am a chemist trying to understand how the uncertainty principle can be applied to the mechanics of atomic and molecular orbitals in order to have better intuitions about stability and reactivity. ...
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Are the concepts of activation energy and collision theory applicable for this reaction?

This is the reaction: $$\text{2Na(s)}+\text{Cl}_2\text{(g)}\longrightarrow \text{2NaCl(s)}\tag{1}$$ This is a reaction between a solid (sodium metal) and a gas (chlorine gas). According to Britannica, ...
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Is ionization energy non-negotiable?

$$\text{2Na(s)}+\text{Cl}_2\text{(g)}\longrightarrow \text{2NaCl(s)}\tag{1}$$ This is a spontaneous reaction ($\Delta G<0$). 2 Na atoms donate 2 electrons to 2 Cl atoms. However, Na still has a ...
2 votes
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How does the concept of activation energy work for interatomic collisions?

Say we have a Lennard-Jones -esque potential for colliding atoms. Say this potential admits a bound state at a lower energy than the kinetic energy of the colliding atoms. So forming this molecule ...
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Does the copper normalize?

I am reading Concepts of Elemental Particle Physics. In it, it describes what happens when a high energy muon is shot into a copper rod. An electron is is knocked out of its orbit and and photons ...
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Excitation of electrons from $3p$ to $3d$ in sulphur

In my book it is shown that sulphur in its excited state forms 6 covalent bonds with Fluorine to form SF6 but after the electron is excited does it not dexcite from $3d$ back to $3p$ and $3s$ by ...
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Why do some atoms like Mg have several ionization energy levels?

In Dopant Energy Levels in Crystalline Silicon (which asks for a password, but is partially readable if you click "cancel") appears the following image and caption: Figure 2777b shows the ...
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Schrodinger operator with matrix potential and Green's function

Clearly Schrodinger operators with matrix potentials appear very naturally in molecular dynamics/quantum chemistry, particularly when considering a crude adiabatic basis or diabatic basis for an ...
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Why is octaoxygen diamagnetic?

I tried considering that according to LCAO-MO theory $O_2$ is paramagnetic, which is confirmed by experimental evidence. Since octaoxygen has the crystal structure in figure, I thought there is a kind ...
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On non-existence of molecular helium (and or why that's equivalent to bond order zero)

Why does molecular orbital theory (MOT) imply that molecular helium does not exist? All answers I found in the web use following two standard arguments, but I not see why these are sufficient to ...
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Who first modelled water as a tetrahedron?

Who first modelled water as a tetrahedron? In this model the oxygen is at the center and the two hydrogens are at the vertices (I think, or maybe somewhere along the edges?). Source This gives the ...
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What prevents us from designing material or catalysts to meet the custom requirements? [closed]

From the perspective of physics, everything is made of atoms, ions, electrons, etc. Since we know the basic interaction between elementary particles, it might be possible to design customized ...
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Atom orbitals physics vs. chemistry

Why draw chemists always $|2p_x\rangle$, $|2p_y\rangle$ and $|2p_z\rangle$ orbitals instead of $|2,1,m\rangle$? Since $|2p_x\rangle$ or $|2p_y\rangle$ are a superposition of energy eigenstates they ...
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Ultra-Low Temperature semiconductors

What benefits does cooling semiconductors have for technology or any other innovations? I understand semiconductors can become good conductors at high temperatures which are ideal for everyday things ...
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Why does inversion symmetry disallow valence band maximum (VBM) to conduction band minimum (CBM) electronic transitions?

I have somewhere read that due to inversion symmetry in the crystal structure the electronic transition occurs from some bands below VBM and therefore optical band gap comes into the picture with a ...
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Cooperative orders

I am familiar with the more "traditional" types of order and their corresponding degrees of freedom one might find in a many-body system, such as crystalline (translational d.o.f.), ...
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What steps are exact in Born-Oppenheimer and adiabatic approximation?

I am reading about adiabatic and Born-Oppenheimer approximation and I can't understand what steps are exact and what steps are approximations. Both these approximations are based on the idea that as ...
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1 answer
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Quantum mechanical model of benzene ring [closed]

The infinite square well scenario can be used to model the $\pi$-electrons of a benzene ring. It can be shown that the eigenfunctions of the ring can be written as $\Psi_{n}(x) = \frac{1}{\sqrt{L}}e^{\...
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Solving to get the kinetic energy integral for restricted closed shell hartree fock calculations

The Kinetic energy integral given in the book Modern Quantum Chemistry by Attila Szabo and Neil Ostlund is given by (Appendix A eqn A.10) $$ \left(A\left|-\frac{1}{2} \nabla^{2}\right| B\right)=\int d ...
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Why does a neutral atom have no external electric field?

I've been trying to find an answer to this for some time now. In advance, I imagine the orbital model, nevertheless I cannot imagine that if I am for example closer to a side of the atom, the dipole ...
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Showing that the creation operator is a spin tensor operator

In the second quantization formalism of quantum chemistry, according to the book 1 on page 43, the creation operators $a_{p,\beta}^{\dagger},a_{p,\beta}^{\dagger}$ satisfy the relations $[\hat S_\pm,...
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How to express atomic states 1S, 1D, 3P in terms of spherical harmonics or cubic harmonics?

Textbook state that, because of Pauli principle and anti-symmetry of wave-function, only 1S, 3P, 1D with totally $C_6^2=15$ states are allowed for 2 electrons $np^2$ state. My question is how to ...
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A poorly posed time dependent perturbation benzene type ring question

In my first year masters QM class my professor recently mentioned an example that he said he would either give on an assignment or possibly put on our exam. We have all our assignments now and it hasn'...
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Probabilities fall outside the differential?

A few years ago I had a conversation with a physical chemist, and one of her comments still lingers in my memory. Our conversation was about Quantum Chemistry. In response to my commenting on the ...
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